All right, now Christiaan, the second child. The first thing we really know of him is in the mid 1640s, 1645, 46. That means he's 15, not quite going to college. He derives the Galilean law of free fall, and his father, not being sure what to do with it, sent it off to Mersenne.
His father knew a lot of people, knew Descartes, like maybe 50 or 60 letters from Descartes are to Huygens, they're all to Constantine. Christiaan met Descartes in the family home because Descartes would visit, Rembrandt would visit. His father was a decent painter, by the way, but not a Rembrandt, needless to say.
But he sent it off to Mersenne and Mersenne looks at it, sends back a nice note saying, I like your proofs better than the ones in this book, but the book, of course, is Two New Sciences. Unfortunately it's all been published already. And then Mersenne took him under his wing for a couple years.
When Mersenne then died in 1648, he made sure Gassendi paid good attention to young Christiaan Huygens. Christiaan went to University of Leiden for his first two years in college, where he studied under van Schooten, the person who put out Descartes' Geometry in Latin with all this extensions of solved problems.
Several of the solved problems in the rest of it are all by van Schooten or his students. Some of them are by Christiaan himself as a student of van Schooten. His last two years though, his father decided to start a new national university called the University of Orange.
And his father said, you can sort of picture this, now that I've started a new university, maybe you should go there and finish your undergraduate career. So he ends up finishing at the new University of Orange. That's obviously a translation. His first publication, 1651, that makes him 22 years old essentially at the time, theorems about the quadrature of hyperbolas, ellipses and circles.
Quadrature is what we mean by integral. Quadrature, is identifying the equivalent square area to an area under a curve. So you'll hear about quadrature all through, the term integral's an 18th century term. And so at this juncture he's the expert on areas under hyperbolas. Which is very important because it's related to logarithms, as you'll see as we go on.
In 1655 he goes to Paris for the first extended stay. Gassendi immediately introduces him into the discussion group Mersenne had started, and he becomes rather quickly the central figure. It's at that time that he announces that he's discovered a satellite of Saturn, the first satellite anybody discovered of Saturn.
And the first announcement is actually to this discussion group, which again I remind you is a male/female discussion group satirized by Moliere in the Learned Ladies, but it's quite an impressive intellectual group. That's 1656. While he was in Paris, he learned of the work that was being done by Fermat and Pascal on probabilities.
So when he got back to Holland in 1657, he wrote the first textbook that's a tract on, in effect, the calculation for games of chance. And it's the first textbook on probability theory, it remains about the only textbook until the 1690s, it's constantly quoted during the period. It's not very long, it was actually published as an addendum to a book by van Schooten.
The nice thing about it, it does everything in terms of expectation. And I don't know that anybody else had formulated probability in games of chance in terms of what we now call expected value. But he does this all the way throughout, and the literal translation would be expectation.
So that's 1657, he doesn't do anything significant more with probability theory after that. Though his younger brother does, looking at actuarial tables and, in effect, applying the statistics to annuities. Trying to figure out what the right return on an annuity should be, so that Holland, or in this case I think it was Amsterdam, doesn't go broke.
Horologium is a book about clocks. I'm gonna pass around, this is from Leiden, the Boerhaave Museum, which is the principal museum for Huygens' stuff. All of Huygens' papers are in the University of Leiden. And it'll show, this is just a catalog of clocks, a large number of which are Huygens'.
In 1658, Huygens invented, and this is very controversial, invented the pendulum clock. Now, what's controversial about it? Galileo had designed a pendulum clock, the trouble was, it didn't keep good time. Robert Hooke had done the same, and it didn't keep good time. So when Huygens comes along and produces a pendulum clock that stays accurate, I'll give the numbers.
Prior to Huygens, clocks in observatories were good to within plus or minus 15 minutes per 24 hours. After Huygens, it's almost unheard of to have an error in a 24 hour period as large as 15 seconds. The norm becomes three or four seconds in a 24 hour period, and that's a fluctuating temperature effect.
That's an enormous change in observational astronomy, cuz you now have clocks that you can totally rely on. You can count the number of minutes on the clock from when one star to the next goes by. You don't have to sit there and do measurements and inferences. So he publishes, in 1658, the Horologium.
I'll show you in a minute, in effect, the kind of clock he had, etc. 1659 is Systema Saturnium. It's the one where he finally identifies that Saturn has rings. And we'll see it two weeks when we resume in this course. It's a lovely piece of detective work, and that sort of ends his career in astronomy in 1659.
You see there's a hiatus of 14 years there, where he doesn't publish a lot. There are some publications, he is producing major stuff at that time, but he's not putting it out in public for a couple reasons. It turns out he had this dream that he was gonna pull all of his work in mechanics together, and publish it as, the treatise on mechanics at the time.
And then Newton published the Principia, and he didn't do that. Instead, most of his work on mechanics got published posthumously. And that's the bottom thing here. Horologium Oscillatorium, Oscillating Clocks is what it's called. I've chosen to put the whole book in English available in Class 10, not under supplementary material, just stuck it in there in case anybody wants to look at it.
There are many ways to describe it. The way I usually describe it is if Newton had not published the Principia, it would be the most important publication in mechanics in the 17th century, hands down. There's nothing else even in the same ballpark, and I'll show you why as we go on.
As I said when I was starting the class, Newton singles it out as preparation for reading the Principia. And the Principia is really modeled on it in many ways. It's a spectacular book. And again, there's a hiatus. What's happening during this time? Well, his first visit to London is in 1660.
While in London he discovers Horrocks, by the way, he's there for two years, discovers Horrocks, enters into the discussion group. When they decide, we'll talk about this in two weeks, when they decide to create the Royal Society, what the actual story here, I've already mentioned they had this invisible university in England doing science.
And when Charles was restored to the throne, the Church of England regained control of the universities. So Boyle, Hooke, Watkins, Christopher Wren, and John Wallace, these are the principle names, go to the new king asking to set up a new university. And the new king doesn't give them a new university.
He gives them enough money to turn their discussion group into a regularly meeting society, the Royal Society, which has met more or less biweekly except summers since 1663. The initial members you'll see next week. Huygens was the sole foreign member of it, right from day one. That tells you already at age, let's see, what's he gonna be at that point?
Roughly 24, is that right? No, 34. At 34 he's already recognized as the leading scientist in the world. Then Colbert decides, Colbert is a major figure behind the throne of Louis XIII in France, and basically he decides that if England's gonna have a Royal Society, France has to have something like it.
So he goes to Louis and Louis is more generous with his money, he decides to set up an institute. It's still called the French Academy, at that time it was called the Royal Academy. After the French Revolution it ceased being called the Royal Academy, but it's still the French Academy of Sciences.
It's been essentially continuous since 1666. Colbert approached Huygens, asking if he would be willing to be part of this. This is a building set aside with roughly 12 to 15 academicians who are doing the leading science in France at the time. They live together, they work together all the time.
An observatory is set up not too far away within walking distance. And Huygens said yes to Colbert and was there from 1666 til 1681. And in a way, the French Academy was built around him. That is, he was the giant in the world, and so he was the central figure, other than he and Cassini didn't get along.
Cassini got appointed the Royal Astronomer and Cassini seems to have been somewhat jealous of Huygens. So that's the other reason Huygens quit messing around much with astronomy, he just let Cassini go off. But during this time, he's actively giving talks and working within the context of the French Academy, and stays there right through late 1670s.
He had, I don't know what the proper description of the disease is, one of his biographers suggests he was not totally mentally stable. I see no evidence of that whatsoever, but he did get periods of very painful migraines that would last months. And he would normally retreat to their summer home in Voorburg, which is not far from The Hague, it's a beautiful place, it's now a museum, and stay there til he felt better.
And this time, Colbert died and he was told, you best not come back to France. It's no longer a healthy place for a Protestant to be. Just to give you a slight feel, Horologium Oscillatorium is dedicated to Louis XIV the Sun King. At the time it was dedicated and published, Holland was at war with France.
And who was leading the war in Holland? Christiaan Huygens' father, okay, so this is a touchy situation. And Colbert was in effect protecting him saying, he doesn't care about politics leave him alone. But he never returned to France after 1681. Continued to converse with them and have publications coming out of the Academy, but never went back to France.
His next major work is published in two pieces. This is the facsimile edition of the publication of The Treatise on Light. It's what Huygens is most famous for now, namely the wave theory of light. It's the first full development of a wave theory of light, mathematical development. It's not transverse waves, it's longitudinal waves.
But it's very much a quite substantial development. And the other is Discourse on the Cause of Gravity. That's going to be very interesting to us at the end of the next term because of the last third of it is a systematic critical commentary on Newton's Principia. This is the world's leading scientist devoting some 25 pages to critically evaluating what Newton has and has not accomplished in the Principia.
So it was the most important assessment of the Principia. Those came out in February of 1690. He died in 1695, not that old. As you see, summer of 1695. And Holland put out, two people, Devulder and 's Gravenzande, put out his collected, the papers he had never published.
And then the Dutch government starting, I think it's 1890, put out his collected works, which are about 70% of the total notebooks. That is, there's a lot of material in the notebooks that have not been published. And what's the number? I think it's 26 volumes of this size?
21? All right, 21 volumes roughly three inches thick. I'll bring one in, I have some of them in my office. So this is somebody who did a huge amount of work over a long period of time, that we're gonna be seeing just part of tonight.
We'll see more of it after we read the Principia because Discourse on the Cause of Gravity is gonna be significant. Let me stop there in case anybody has any questions about just the biography. I should say one other thing. He seems to have been a genuinely nice human being.
Which is he and Kepler seem to be the only ones we're gonna be talking about in major figures who, and I'll give you my best example of that. Huygens, excuse me, Hooke attacked him kind of mercilessly over the claim that he had the first successful pendulum clocks. And Hooke had never even produced a clock.
What Huygens did once he designed it was hand it to clockmakers and they produced them in bulk. Huygens was the engineer who designed it, he was happy to turn it over then. And he let them make all the profits, by the way, patents were not in effect, etc.
But Hooke was very, very nasty about it. So there's a letter from Christiaan to his father when Hooke's book, you'll see it next class, Micrographia comes out. And the letter says, this man Hooke, referring to, I'm now paraphrasing, is a real jerk. But when you look at the drawings in this book, you can't help but really admire him.
And that seems to be the character of Christiaan Huygens. He could be offended by people, and there'll be a story about his being offended tonight. But it's not the sort of person who goes around nastily treating other people, he was a really nice human being. He never married, I have no idea what that says.
I know of his showing no interest in any sort of social life other than the life of science in his entire life but that doesn't mean anything. Most of the detailed information about his life is in Dutch and I don't read Dutch. If it weren't for the Dutch government putting out all this work, it's more than 50 years, it's almost 60 years, yeah.
Some 60 years, you can get it in my notes, I reference the whole of the publication. If it weren't for the Dutch government putting it out and then giving those away, they gave the collected volumes to libraries for free in an effort to promote this great scientist they had.
If it weren't for that, I'm not sure what scholarship on Huygens would be like, because there is a little too much in Dutch, simply put. The other thing I can say about him is when I go through his notebooks, I have a copy, I don't have his notebook.
I have a copy of his notebooks while he's reading the Principia. And first of all, he's the one person I know totally understood the Principia. No problem at all, he went right through it. But what's really striking to me as a trained engineer is, his notebooks are an engineer's notebooks.
He seems to have thought like an engineer all the time, at least my sense of what an engineer is. When I look at Newton's manuscripts, I have to really work to sort out what's going on. He doesn't think like me, he doesn't think like an engineer. Huygens is constantly thinking of devices and things like that, and you'll see it several times tonight.